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Synthese

, Volume 81, Issue 3, pp 283–312 | Cite as

Gibbs' paradox and non-uniform convergence

  • K. G. Denbigh
  • M. L. G. Redhead
Article

Abstract

It is only when mixing two or more pure substances along a reversible path that the entropy of the mixing can be made physically manifest. It is not, in this case, a mere mathematical artifact. This mixing requires a process of successive stages. In any finite number of stages, the external manifestation of the entropy change, as a definite and measurable quantity of heat, isa fully continuous function of the relevant variables. It is only at an infinite and unattainable limit thata non-uniform convergence occurs. And this occurs when considered in terms of the number of stages together with a ‘distinguishability parameter’ appropriate to the particular device which is used to achieve reversibility. These considerations, which are of technological interest to chemical engineers, resolve a paradox derived in chemical theory called Gibbs' Paradox.

Keywords

Continuous Function Chemical Engineer Finite Number Successive Stage Entropy Change 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Kluwer Academic Publishers 1989

Authors and Affiliations

  • K. G. Denbigh
    • 1
    • 2
  • M. L. G. Redhead
    • 1
    • 2
  1. 1.Department of History and Philosophy of Science King's College (KQC)University of LondonU.K.
  2. 2.Department of History and Philosophy of ScienceUniversity of CambridgeCambridgeU.K.

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